Large time behavior of solutions for degenerate p-degree Fisher equation with algebraic decaying initial data

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:448

Article

He, Junfeng¹  Wu, Yanxia²  Wu, Yaping^1,3 

[1] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

[2] Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan, Peoples R China

[3] Beijing Ctr Math & Informat Interdisciplinary Sci, Beijing 100048, Peoples R China

关键词: Degenerate Fisher equation;    Non-exponential decay;    Traveling fronts;    Lyapunov stability;    Spreading speed;   

DOI  :  10.1016/j.jmaa.2016.10.037

来源: Elsevier

【 摘 要 】

This paper is concerned with the large time behavior of solutions to the one-dimensional degenerate p-degree Fisher equation, where the initial data are assumed to be asymptotically front-like and to decay to zero non-exponentially at one end. By applying sub-super solution method we first prove the Lyapunov stability of all the wave fronts with noncritical speeds in some polynomially weighted space. Further, by using semigroup estimates, sub-super solution method and the nonlinear stability of the traveling waves, we obtain the asymptotic estimates of the solutions which indicate that the solution still moves like a wave front and the asymptotic spreading speed of the level set of the solution can be finite or infinite, which is solely determined by the detailed decaying rate of the initial data. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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